There is no such thing as the world’s largest math problem, as the size and complexity of mathematical problems are subjective and can vary depending on the field and context.
So let us take a closer look at the inquiry
Mathematical problems can vary greatly in size and complexity, which makes it impossible to point to a definitive “world’s largest math problem.” In fact, mathematician Keith Devlin has stated that “large scale computation has made it possible to solve problems that would not even have been recognized as problems, let alone formulated, just a generation ago.” That being said, there are certainly some monumental mathematical problems that have captured the attention of the mathematical community and the general public.
One such problem is the Riemann Hypothesis, which is widely regarded as one of the most important unsolved problems in mathematics. The hypothesis, put forth by Bernhard Riemann in 1859, concerns the distribution of prime numbers and involves complex analysis and number theory. If proved true, the Riemann Hypothesis would have significant implications for cryptography and computer science.
Another famous problem is Fermat’s Last Theorem, which was famously solved by Andrew Wiles in 1995 after more than 350 years of attempts by various mathematicians. The problem involves finding three positive integers that satisfy the equation a^n + b^n = c^n, where n is an integer greater than 2.
In addition to these well-known problems, there are a multitude of other mathematical puzzles and challenges that continue to fascinate and inspire mathematicians today. Some other examples include:
- The P vs. NP problem, which concerns the efficiency of algorithms and has significant implications for computer science and cryptography.
- The Birch and Swinnerton-Dyer Conjecture, which concerns elliptic curves and their associated L-functions.
- The Hodge Conjecture, which relates to algebraic geometry and topology.
- The Collatz Conjecture, which involves recursive sequences and has puzzled mathematicians for decades.
Despite the lack of a definitive “world’s largest math problem,” the sheer breadth and depth of mathematical challenges continues to captivate researchers and inspire new avenues of inquiry.
| Problem | Description | Importance |
|---|---|---|
| Riemann Hypothesis | Concerns the distribution of prime numbers and has significant implications for cryptography and computer science. | Widely regarded as one of the most important unsolved problems in mathematics. |
| Fermat’s Last Theorem | Involves finding positive integers a, b, and c that satisfy the equation a^n + b^n = c^n, where n is an integer greater than 2. | Solved by Andrew Wiles in 1995 after more than 350 years of attempts by various mathematicians |
| P vs. NP problem | Concerns the efficiency of algorithms and has significant implications for computer science and cryptography. | Considered one of the most important problems in computer science |
| Birch and Swinnerton-Dyer Conjecture | Concerns elliptic curves and their associated L-functions. | Implications for number theory and algebraic geometry |
| Hodge Conjecture | Relates to algebraic geometry and topology. | Implications for algebraic geometry and topology |
| Collatz Conjecture | Involves recursive sequences and has puzzled mathematicians for decades. | Considered one of the most notorious unsolved problems in mathematics |
See a video about the subject.
YouTuber Michelle Khare attempts to solve the world’s longest math problem consisting of 10,000 digits on a scissor lift within six hours. She successfully solves a 10-digit problem, then a 100-digit problem while struggling with the last few lines, followed by a thousand-digit problem that she completes. Despite being pelted with water balloons for every wrong answer, Michelle uses a Chinese abacus and finishes the entire problem in 5 hours and 42 minutes, with the help of her team who check her work. The YouTuber expresses their support for those struggling with math and their pride in Michelle’s completion of the problem, and the video concludes with Michelle shedding tears of joy.
Further responses to your query
Mathematicians worldwide hold the Riemann Hypothesis of 1859 (posed by German mathematician Bernhard Riemann (1826-1866)) as the most important outstanding maths problem. The hypothesis states that all nontrivial roots of the Zeta function are of the form (1/2 + b I).
One of the most elusive maths problems has been solved by three computer scientists and a supercomputer. The proof to Boolean Pythagorean triples problem comes in a 200-terabyte file, making it the world’s largest math proof.
The largest-ever math problem called the Boolean Pythagorean triples problem has been solved by a supercomputer and three computer scientists.
That’s the size of the file containing the computer-assisted proof for a mathematical problem that has boggled mathematicians for decades—known as Boolean Pythagorean triples problem.
This probably isn’t the longest equation, but the Lagrangian for the standard model (which describes all observed physical processes, sans gravity, given locality, causality, Lorentz invariance, and known physical data since 1860) is moderately lengthy:
(TeXified by T.D. Gutierrez from an appendix in Martinus Veltman’s Diagrammatica: http://nuclear.ucdavis.edu/~tgutierr/files/stmL1.html )